Answers to ECON3107 assessment 1

Answers to ECON3107 assessment 1 - 0 0 1.05 0.90...

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Question 1: >> Q= [20 60 45; 20 30 5; 20 5 0] >> ps= [18 19 8] >> P_atom= ps*inv (Q) >>P_atom = 0.1500 0.2500 0.5000 >>P_atom * [80 50 25]’ = 37PA (Value of the Apple Tree) i) 0.15 is the arbitrage free price of the atomic securities in good weather, 0.25 refers to the arbitrage free price of the atomic securities when the weather is fair and 0.50 implies to the arbitrage free price of the atomic securities when the weather is bad. ii) The arbitrage free price of an apple tree is 37 PA. iii) The discount factor works out to be 0.9 (sum of the atomic security prices). It tells us the value of an apple in the next period in terms of present apples. iv) For the investor to be able to obtain 30GA, 30FA, and 50BA, he or she needs to invest 2.7353 PA in the bond, short sell 0.9412 PA in the stock and invest 0.7059PA in security C. The arbitrage free price for the security is 37. v) Question 2 i) Q matrix= 1.05 1.30 -1 -1 0 0 1.05 0.90 0 0 -1 -1 0 0 1.05 1.30 0 0 0 0 1.05 0.90 0 0 0 0 0 0 1.05 1.30 0 0
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Unformatted text preview: 0 0 1.05 0.90 Corresponding price vector (ps) = ( 1 1 0 0 0 0 ) ii) p_atom = ps * inv (Q) p_atom = ( 0.3571 0.5952 0.1276 0.2126 0.2126 0.3543) iii) Assuming that I have purchased the European call option, iv) We can price the option by constructing a portfolio of elemental payment combinations that generates the same vector c. It follows from the no-arbitrage condition (as well as LOP) that the replicating portfolio and option should have the same price. In fact, once we have calculated the atomic price vector, it is not even necessary to construct a replicating portfolio. The arbitrage-free price of the option can be calculated directly by simply multiplying the atomic price vector by the time-state vector, c, implied by the option (assuming it is exercised optimally). Call = ( 0 0 0.64 0.12 0.12 0) P call= p_atom * call p_call = 0.1327 v) Assuming that I have purchased the European put option vi) Call= (0 0 0 0 0 0.24) P call= p_atom * call p_call = 0.0850...
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Answers to ECON3107 assessment 1 - 0 0 1.05 0.90...

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